The determination of dynamic aperture is a critical issue in circular accelerator. In this paper, we solved the equation of motion including non-linear forces by using successive linearization method and got a criterion for. the determining of the dynamic aperture of the machine. Applying this criterion, a storage ring with FODO lattice has been studied. The results are agree well with the tracking results in a large range of linear turn (Q). The purpose is to improve our understanding of the mechanisms driving the particle motion in the presence of non-linear forces and got another mechanism driving instability of particle in storage ring-parametric resonance caused by "fluctuating transfer matrices" at small amplification.